Global voltage dynamics: study of a generator with voltage control, transmission, and matched MW load

A rudimentary but representative model for voltage dynamics of a power system is studied. A comprehensive analysis of the different types of dynamic behavior across both state and parameter space is given with control gains and load varied. The model is subject to algebraic constraints in the form of load flow equations. A singular transformation changes the resulting singular model into a smooth dynamical system, facilitating the analysis. Singular manifolds in the state space and bifurcation manifolds in the parameter space turn out to be the principal and interacting determinants for the problem. Both local and global bifurcations play vital roles. Some of the bifurcations are directly connected to the singularity. The maximum practical load is increasing with control gain, but the region of transient stability, which is a halfspace at low gains, gradually shrinks down to a point at the Hopf bifurcation. The characteristics of stability boundaries are observed, and the loosely understood term of voltage collapse is classified into well-defined types. Simulations are used to illustrate the mathematical results